Bitap algorithm
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- Snippet from Wikipedia: Bitap algorithm
The bitap algorithm (also known as the shift-or, shift-and or Baeza-Yates-Gonnet algorithm) is an approximate string matching algorithm. The algorithm tells whether a given text contains a substring which is "approximately equal" to a given pattern, where approximate equality is defined in terms of Levenshtein distance – if the substring and pattern are within a given distance k of each other, then the algorithm considers them equal. The algorithm begins by precomputing a set of bitmasks containing one bit for each element of the pattern. Then it is able to do most of the work with bitwise operations, which are extremely fast.
The bitap algorithm is perhaps best known as one of the underlying algorithms of the Unix utility agrep, written by Udi Manber, Sun Wu, and Burra Gopal. Manber and Wu's original paper gives extensions of the algorithm to deal with fuzzy matching of general regular expressions.
Due to the data structures required by the algorithm, it performs best on patterns less than a constant length (typically the word length of the machine in question), and also prefers inputs over a small alphabet. Once it has been implemented for a given alphabet and word length m, however, its running time is completely predictable – it runs in O(mn) operations, no matter the structure of the text or the pattern.
The bitap algorithm for exact string searching was invented by Bálint Dömölki in 1964[1][2] and extended by R. K. Shyamasundar in 1977[3], before being reinvented by Ricardo Baeza-Yates and Gaston Gonnet[4] in 1989 (one chapter of first author's PhD thesis[5]) which also extended it to handle classes of characters, wildcards, and mismatches. In 1991, it was extended by Manber and Wu [6][7] to handle also insertions and deletions (full fuzzy string searching). This algorithm was later improved by Baeza-Yates and Navarro in 1996.[8]
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